Lectures related to Function of a real variable

Explores definitions and examples of real functions of a real variable.

Explores interpolation spaces in Banach spaces, emphasizing real continuous interpolation spaces and the K-method.

Explores continuity and limits of real functions, including examples and the concept of uniform continuity.

Covers real numbers, sequences, series, functions, limits, derivatives, Taylor series, integrals, and more.

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Covers the concept of partial derivatives of higher order and their applications in various contexts.

Covers the definition of double integrals for functions of two variables over a domain in the plane R^2.

Covers the Continuity Theorem for functions dependent on a parameter, proving the continuity of a function g.

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Explores real functions, composition, and limits, including algebraic operations and sequence characterization.

Discusses the uniqueness of implicit functions solutions and surfaces described by equations.

Explores curve length, function definition, continuity, derivatives, integrals, and graphical representations of functions in two variables.

Explores the fundamental principle of the recurrence method and differential calculus of functions of several variables.

Covers definitions and examples of real functions of several real variables, including limits and visualization techniques.

Explores differentiable functions, gradients, and tangent planes in two-variable functions.

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Covers derivatives, differentiability, and tangent planes for functions of one and two variables.

Covers the discussion of real functions and the concept of limits.

Covers the integration of functions in several variables, Darboux sums, and Fubini's theorem on a closed box.